Passive Circuit Analysis with LTspice®: An Interactive Approach

✍ Scribed by Colin Percy May

• Publisher: Springer International Publishing
• Year: 2020
• Tongue: English
• Leaves: 776
• Category: Library

✦ Synopsis

This book shows readers how to learn analog electronics by simulating circuits. Readers will be enabled to master basic electric circuit analysis, as an essential component of their professional education. The author’s approach enables readers to learn theory as needed, then immediately apply it to the simulation of circuits based on that theory, while using the resulting tables, graphs and waveforms to gain a deeper insight into the theory, as well as where theory and practice diverge!

✦ Table of Contents

Foreword
Contents
Chapter 1: LTspice Essentials
1.1 Introduction
1.2 Representing the Circuit
1.3 Drawing Conventions
1.3.1 Component Symbols
1.3.1.1 Voltage Sources
1.3.1.2 Resistors
1.3.1.3 Current Sources
1.3.1.4 Ground Connection
1.3.1.5 Connections
1.4 Drawing the Circuit and Ohm´s Law
1.4.1 Drawing the Circuit
1.4.1.1 The Opening Screen
1.4.2 Placing Components
1.4.2.1 Resistors
1.4.2.2 Voltage Source
1.4.2.3 Ground
1.4.2.4 Alternative Symbols
1.4.2.5 Component Names
1.4.3 Connecting the Circuit
1.4.4 Adding Values
1.4.4.1 Resistors
1.4.4.2 Voltage Sources
1.4.5 Editing the Circuit
1.4.6 Annotations
1.4.6.1 Edit Text on the Schematic Dialogue
1.5 Running the Simulation and the .op Command
1.5.1 Simulation Results
1.5.1.1 Voltage, Current and Power Probes
1.5.1.2 The Text Document (.log)
1.5.1.3 The .NET File
1.5.1.4 The RAW Files
1.6 Sweeping Voltage and Current Sources
1.6.1 DC Sweep Command
1.6.2 The Trace Window
1.6.2.1 Adding Traces
1.6.2.2 Editing Traces
1.6.2.3 Changing the Colours
1.6.2.4 Showing the Results
1.6.2.5 Saving the Results
1.6.2.6 Saving Plot Settings (Plt´ File) 1.6.2.7 Printing 1.6.3 The Control Panel 1.6.3.1 Basic Options 1.6.3.2 Drafting Options 1.6.3.3 Waveform Options 1.6.3.4 Compression 1.7 Changing the Value of a Component During Analysis 1.7.1 Using Parameters.param´
1.7.1.1 Syntax
1.7.1.2 Usage
1.7.2 Step Command .step´ 1.7.2.1 Syntax 1.7.2.2 Usage 1.7.2.3 Showing the Result 1.7.3 Production Yields 1.7.3.1 Statistical Distribution 1.7.3.2 Monte Carlo Analysis 1.8 SPICE 1.8.1 Schematic Capture 1.8.1.1 Learning Curve 1.8.1.2 The Component Palette 1.8.1.3 Accessing the Results 1.8.1.4 Saving the Results 1.8.2 SPICE Analysis 1.8.2.1 Numerical Integration Methods 1.8.3 Performance 1.8.3.1 Accuracy 1.8.3.2 Speed 1.8.3.3 Omissions 1.8.3.4 Enhancements 1.9 Summary Chapter 2: DC Circuits 2.1 Introduction 2.2 Kirchhoff´s Laws 2.2.1 Resistors in Parallel and Kirchhoff´s Current Law 2.2.1.1 A Moving Coil Ammeter 2.2.2 Resistors in Series and Kirchhoff´s Voltage Law 2.2.2.1 A Moving Coil Voltmeter 2.2.2.2 Meter Loading 2.2.2.3 A Moving Coil Ohmmeter 2.3 Some Useful Circuits 2.3.1 The Potential Divider 2.3.2 The.measure´ (.meas) Directive
2.3.2.1 Measure MAX, MIN
2.3.3 Maximum Power Transfer
2.3.3.1 Theory
2.3.3.2 The .step´ Command 2.3.3.3 The .meas Directive (TRIG,TARG) 2.3.4 The Wheatstone Bridge 2.3.4.1 The Kelvin Double Bridge 2.3.4.2 The Murray and Varley Loop Tests 2.4 More Analysis Methods 2.4.1 Superposition 2.4.2 The Thevenin Model 2.4.3 The Norton Model 2.4.3.1 Wheatstone Bridge Sensitivity 2.5 Attenuators 2.5.1 The L-Attenuator 2.5.2 TheT´-Attenuator
2.5.2.1 Impedance Matching
2.5.2.2 The Bridged-T Attenuator
2.5.3 The Pi-Attenuator
2.6 Delta-Star Conversion
2.6.1 Delta-Star Conversion
2.6.2 Star-Delta Conversion
2.7 The Thermocouple
2.8 Metrology
2.8.1 Voltage Standard
2.8.1.1 Equipment Voltage Standard
2.8.1.2 Voltage Divider
2.8.2 Resistance
2.8.2.1 Interrelationship of Standards
2.9 Practical Considerations
2.9.1 Fixed Resistors
2.9.1.1 Mounting Methods
2.9.1.2 Resistor Types
2.9.1.3 Resistor Series
2.9.1.4 The Resistor Colour Code
2.9.1.5 The Resistor Letter and Number Code
2.9.2 Variable Resistors
2.10 Summary
Chapter 3: Non-linear Resistors
3.1 Introduction
3.2 The LTspice Resistor
3.2.1 The Component Attribute Editor
3.3 Variable Resistors
3.3.1 Potentiometers
Example - A Linear Potentiometer
Example - A Sine Potentiometer
Example - A Logarithmic Potentimeter
3.4 Resistor Temperature Effects
3.4.1 Adding Temperature Coefficients
3.4.2 Temperature Analysis
Temperature Analysis Using the .step´ Command Changing the Resistor´s Reference Temperature Modelling Self-Heating 3.5 The Platinum Resistance Thermometer 3.5.1 Arbitrary Temperature Coefficient 3.5.2 The Cubic Equation Reading the Temperature 3.6 Thermistors 3.6.1 Temperature Measurement Using NTC Thermistors The Beta Relationship Steinhart-Hart Equation Self-Heating 3.6.2 Temperature Measurement Using PTC Thermistors Linearizing the Probe 3.6.3 Circuit Protection Residual Current Devices, Circuit Breakers and Fuses In-Rush Limiting Over-current and Over-voltage Protection 3.7 Voltage Variable Resistors (Varistors) 3.7.1 Basic Models The LTspice Model LittelFusePulseguard´
The LittelFuse SPICE Varactor
The AVX SMD Varistor MAV Series
Automotive EMC Testing ISO 16750-2 and ISO7637-2
3.8 Photoconductive Cells
3.8.1 Illumination Characteristics
Illumination Standard
3.8.2 Photocell Response
Spectral Response
Dark Resistance
Response Time
Temperature Effects
3.8.3 SPICE Models
3.9 Other Variable Resistors
3.9.1 Time Variable Resistors
3.9.2 Frequency Variable Resistors
3.10 Summary
Chapter 4: Models and Sub-circuits
4.1 Introduction
4.2 Symbols
4.2.1 Alternative Symbols
4.2.2 Creating the Drawing
4.2.2.1 Use an Existing Symbol
4.2.2.2 Modify an Existing Symbol
4.2.2.3 Downloading from an Internet Site
4.2.2.4 Automatically Creating a Symbol
4.2.2.5 Drawing a New Symbol
4.2.3 Adding Pins
4.2.3.1 Placing a Pin
4.2.3.2 Pin Labels
4.2.3.3 Pin Order
4.2.4 Symbol Attributes
4.2.4.1 Symbol Type (1)
4.2.4.2 Prefix (2)
4.2.4.3 Spice Model (3)
4.2.4.4 Value and Value2 (4)
4.2.4.5 SpiceLine and SpiceLine2 (5)
4.2.4.6 Description (6)
4.2.4.7 ModelFile (7)
4.2.5 Saving the Symbol
4.3 Sub-circuits
4.3.1 Sub-circuit Structure
4.3.1.1 The First Line
4.3.1.2 Sub-circuit Identification
4.3.1.3 Sub-circuit Body
4.3.1.4 Models and Other Sub-circuits
4.3.1.5 Ends
4.3.1.6 Exclusions
4.3.2 Downloading Sub-circuits
4.3.2.1 Symbol Files
4.3.2.2 Library Files
4.4 Example Sub-circuits
4.4.1 A Wire-Wound Resistor
4.4.1.1 NetList on the Schematic
4.4.1.2 Sub-circuit from Parts on the Schematic
4.4.1.3 Saving and Testing the Sub-circuit
4.4.2 Potentiometer
4.4.2.1 Symbol (Assembly)
4.4.2.2 Netlist on the Schematic
4.4.2.3 Platinum Resistance Thermometer (PRT)
4.4.2.4 Thermostat
4.4.2.5 A Single-Pole Change-Over Relay
4.4.2.6 Changing Values in a Sub-circuit
4.4.2.7 For Later Chapters
4.5 Summary
Chapter 5: Voltage and Current Sources
5.1 Introduction
5.2 Independent Voltage and Current Source
5.2.1 DC Source
Current Load´´ 5.2.2 AC Analysis AC Amplitude Phase 5.2.3 Voltage Source: Parasitic Properties 5.2.4 Functions (None) Pulse Sine Exponential SFFM (Single-Frequency Frequency-Modulated Source) PWL, PWL File WaveFile Current Source-Table Current Source - Step Current Source - Active Load 5.3 Arbitrary Sources (B) 5.3.1 Constant Power Function Optional Parameters Rounding Functions Limiting Functions Power Functions Random Numbers Logarithmic Functions Trigonometrical Functions Hyperbolic Functions Calculus Miscellaneous Functions 5.4 Dependent Sources 5.4.1 Voltage-Controlled Voltage Sources (E,E2) 5.4.2 Current-Controlled Current Source (F) 5.4.3 Voltage-Controlled Current Source (G,G2) 5.4.4 Current-Controlled Voltage Source(H) 5.5 Summary Chapter 6: AC Theory 6.1 Introduction 6.1.1 Some More `.meas´ Methods Transient Analysis and Compressed Data . meas DERIV AT .meas DERIV WHEN .meas FIND WHEN .meas PARAM .meas AVG, RMS, PP .meas INTEG 6.2 AC Basics 6.2.1 Simple Harmonic Motion 6.2.2 Waveform Synthesis 6.2.3 Sine Wave Parameters Trigonometric Functions Using the Cursor to Measure the RMS and Average Values Average Value Half-Cycle Average RMS Value Power 6.2.4 Adding Sine Waves Resultant Waveform Peak and RMS Value 6.2.5 Partial Sine-Wave Average Value Half-Cycle Average RMS 6.3 Rectangular Waves 6.4 Triangular Waves 6.4.1 Average Value 6.4.2 RMS Value 6.5 Other Waveforms 6.6 Other Forms of Trigonometrical Functions 6.6.1 Series Forms Maclaurin Series The Sine Series The Cosine Series Applications 6.6.2 Exponential Forms Real and Imaginary Numbers Complex and Polar Form The History of e Continuous Interest and e Series Expansion of e Euler´s Relationships Natural Logarithms Trigonometrical Identities The Complex Conjugate Cos(θ)2 + Sin(θ)2 = 1 Sin(2θ) = 2 sin(θ)cos(θ) Cos(2θ) = Cos2(θ)-Sin2(θ) 2Cos(θ)Cos(Phi) = Cos(θ-Phi) + Cos(θ + Phi) Cos(θ + Phi) and Sin(θ + Phi) 6.7 `.four´ Waveform Analysis 6.7.1 Application Adding More Harmonics and Cycles The Effect of Not Using Exact Harmonics 6.8 Summary Chapter 7: Capacitors 7.1 Introduction 7.2 Capacitors 7.2.1 Unit of Capacitance 7.2.2 Energy Stored in a Capacitor 7.2.3 Capacitors in Parallel and in Series 7.2.4 Capacitors in Series Voltage Ratings 7.3 Capacitor Types 7.3.1 Variable Capacitors 7.3.1.1 User Controls 7.3.1.2 Preset Capacitors 7.3.2 Fixed Non-polar Capacitors 7.3.2.1 Ceramic 7.3.2.2 Silver Mica Capacitors 7.3.2.3 Film (Plastic) Dielectric Capacitors 7.3.3 Polar (Electrolytic) Capacitors 7.3.3.1 Aluminium Electrolyte 7.3.3.2 Tantalum Capacitors 7.3.3.3 Super Capacitors 7.3.4 SPICE AC Analysis 7.3.4.1 LTspice AC Analysis 7.3.4.2 Changing the Y-Axis Bode Nyquist Cartesian 7.3.4.3 Changing the X-Axis 7.3.4.4 Changing the View 7.4 Capacitor Models 7.4.1 The LTspice Model 7.4.1.1 Temperature Effects 7.4.1.2 Voltage Effects 7.4.2 Capacitor Losses 7.4.2.1 Capacitor Dissipation Factor (DF) 7.4.2.2 Capacitor Self-Resonant Frequency fr 7.4.2.3 Capacitor Q-Factor 7.4.2.4 Capacitor Impedance 7.4.2.5 Other Measures of Parasitic Properties 7.4.2.6 Capacitor Loss Angle (δ) 7.4.3 Capacitor as Charge 7.4.3.1 Charge = C.f(x) 7.4.3.2 Charge = C.f(time) 7.4.3.3 Charge = C.f(current) 7.4.4 Manufacturer´s Capacitor Models 7.4.4.1 AVX Ceramic Capacitor Model Multilayer Chip Ceramic (MLCC) Capacitor Models 7.4.4.2 SPICE Polar Capacitor Models Nichicon Aluminium Electrolytic Capacitors Tantalum Capacitors 7.5 Time Response of a Capacitor 7.5.1 Capacitor Charging 7.5.1.1 The Time Constant, Rise Time and Fall Time 7.5.2 Capacitor Discharge 7.5.3 Sag 7.5.3.1 Pulse Train Response 7.5.4 Average Voltage 7.5.4.1 Amplitude Modulation Smoothing 7.5.4.2 Pulse Width Modulation Smoothing 7.6 Frequency Response of a Capacitor 7.6.1 Voltages and Currents 7.6.1.1 Reactance and Impedance of a Capacitor 7.6.2 Manual Circuit Analysis 7.6.2.1 Using the Complex Plane 7.6.2.2 Using Complex Numbers 7.7 Frequency Response of Series RC Circuits 7.7.1 Manual Analysis 7.7.1.1 The Decibel 7.7.1.2 The 3 dB Point 7.7.1.3 Relation Between Frequency Response and Time Response 7.7.1.4 Bode Plot 7.7.1.5 Manual Construction 7.8 Summary Chapter 8: RC Circuits 8.1 Introduction 8.2 Simple Capacitor-Resistor Circuits 8.2.1 De Sauty Capacitance Bridge 8.2.1.1 Analysis 8.2.2 Schering Bridge 8.2.2.1 Loss Angle (δ) and Dissipation Factor 8.2.3 The Compensated Potential Divider 8.2.3.1 Analysis 8.2.4 RIAA Filters 8.2.5 Relaxation Oscillator and `sw´ Component 8.2.5.1 Charging Time 8.2.5.2 Using the LTspice Neon Bulb 8.2.5.3 Discharge Time 8.2.6 Tapped Capacitor Impedance Matching 8.2.6.1 Input Admittance 8.2.6.2 Voltage Gain 8.2.6.3 Q-Factor 8.3 Passive Tone Controls 8.3.1 The Big Muff 8.3.2 The James 8.3.3 Baxandall Tone Control 8.4 Noise 8.4.1 Noise Sources 8.4.1.1 Johnson (Thermal) Noise 8.4.1.2 Adding Noise Contributions 8.4.2 LTspice and Noise 8.4.2.1 Noise Settings and Measurements 8.4.3 Noise Generator 8.4.3.1 Using white Arbitrary Source 8.4.3.2 Using a Voltage or Current Source 8.4.4 Noise Reduction 8.5 RC Delay Lines 8.5.1 Elmore Delay 8.5.1.1 Elmore Delay for RC Line 8.5.2 The Uniform RC Line 8.5.2.1 Creating an Instance 8.5.2.2 Placing an Instance 8.5.2.3 Creating Different Instances 8.5.2.4 The URC Parameters 8.6 Thermal Modelling 8.6.1 Heat Transfer Mechanisms 8.6.1.1 Radiation 8.6.1.2 Convection 8.6.1.3 Conduction 8.6.2 Semiconductor Thermal Models 8.6.2.1 Foster Model '.net' Statement 8.6.2.2 The Cauer Model 8.6.2.3 The URC Model 8.6.3 Thermal Models of Buildings 8.7 Summary Chapter 9: Second-Order RC Filters 9.1 Introduction 9.2 The Laplace `s´ Function 9.2.1 Comparison of ω and s Transfer Functions 9.2.2 Poles and Zeros 9.2.3 Types of Poles 9.2.3.1 Pole = (s + a) 9.2.3.2 Pole = s 9.2.4 Types of Zeros 9.2.4.1 Zero = s + a 9.2.4.2 Zero = s 9.2.5 Voltage Gain 9.2.6 Laplace Numerator 9.2.6.1 Laplace Denominator 9.2.6.2 Laplace Fractions 9.3 Two-Port Networks 9.3.1 The `.net´ Directive 9.3.2 H-Parameters 9.3.2.1 H-Parameter Equivalent Circuit 9.3.3 Z-Parameters 9.3.4 Y-Parameters 9.3.5 Scattering Parameters 9.4 Second-Order RC Cascade Networks 9.4.1 General Analysis 9.4.1.1 An Alternative Approach 9.4.1.2 The Transfer Function 9.4.2 Low-Pass Filter 9.4.2.1 Filter Design 9.4.3 High-Pass Filter 9.4.4 Band-Pass Filter 9.4.4.1 Cascaded High Pass and Low Pass 9.4.4.2 Cascaded Two `L´ Filters 9.4.4.3 Band-Pass Filter V3 9.5 LTspiceLaplace´´
9.5.1 The Laplace Transform
9.5.2 Laplace Transform Examples
9.5.2.1 Unit Step Input
9.5.2.2 Time Delay
9.5.2.3 Sine Wave
9.5.2.4 A Decaying Exponential
9.6 Sketching the Bode Plot
9.6.1 Magnitude
9.6.1.1 Initial Value
9.6.1.2 Remaining Values Using Slopes
9.6.1.3 Plotting the Phase
9.7 Band-Stop Filters
9.7.1 A Simple Band-Stop Filter
9.7.2 The Bridged-T
9.7.2.1 General Analysis
9.7.2.2 Notch Filter ω0
9.7.2.3 Notch Depth
9.7.2.4 Q-Factor
9.7.3 Twin-T Filter
9.7.3.1 Filter ω0
9.7.3.2 Notch Depth
9.7.3.3 Time Response
9.7.4 Other Notch Filters
9.8 Summary
Chapter 10: Transmission Lines
10.1 Introduction
10.2 Uniform RC URC´ Line 10.2.1 Syntax 10.2.2 Parameters 10.2.2.1 Global Parameters 10.2.2.2 Diode Parameters 10.3 Transmission Lines 10.3.1 Equivalent Circuit 10.3.2 Analysis 10.4 Lossless Transmission Linetline´
10.4.1 Voltage Reflections
10.4.1.1 Open-Circuit End
10.4.1.2 Matched Impedance
10.4.1.3 Short-Circuit End
10.4.1.4 Mismatch
10.4.2 Current Reflections
10.4.2.1 Open-Circuit End
10.4.2.2 Matched Impedance
10.4.2.3 Short-Circuit End
10.4.2.4 Parameters
10.4.3 Single Mode Behaviour
10.4.3.1 Transient Analysis
10.4.4 Multimode Behaviour
10.4.5 Frequency Response
10.4.5.1 The Simple Explanation
10.4.5.2 Impedance with Non-matched Load
10.4.5.3 Cut-Off Frequency and Bandwidth
10.4.5.4 Spatial Distribution of Voltage and Current
10.4.6 Discrete Lossless Transmission Line
10.4.6.1 Dispersion
10.4.6.2 Impedance
10.5 Lossy Transmission Line
10.5.1 Analysis
10.5.2 The LTspice ltline´ 10.5.3 Discrete Lossy Line 10.6 Summary Chapter 11: Inductors and Transformers 11.1 Introduction 11.2 Magnetism 11.2.1 Magnetic Effects of an Electric Current 11.2.1.1 The Ampere 11.2.2 Inductance of a Solenoid 11.2.2.1 Circuit Symbol 11.3 Inductors 11.3.1 The B-H Curve 11.3.1.1 Magnetic Domains 11.3.2 The Magnetic Circuit 11.3.2.1 The Effect of the Air Gap 11.3.3 Inductor Losses 11.3.3.1 Hysteresis Loss 11.3.3.2 Copper Loss 11.3.3.3 Eddy Current Loses 11.3.3.4 Dielectric Loss 11.3.4 Choice of Magnetic Material 11.3.5 Inductor Design 11.3.5.1 The Inductance 11.3.5.2 Power Handling 11.3.5.3 Core Material Selection 11.3.5.4 The Winding 11.3.6 LTspice Inductor 11.3.6.1 Linear Inductor with Parasitic Resistance and Capacitance 11.3.6.2 LTspice Inductor Loss 11.3.6.3 Behavioural Model of the Flux 11.3.6.4 Hysteretic Core Model 11.3.7 Other Models 11.3.7.1 Jiles-Atherton Model 11.3.7.2 Newport Components Model 11.3.7.3 The Coilcraft Advanced Model 11.3.7.4 The Murata Models 11.3.7.5 The Peretz Model 11.3.7.6 Modelling a Ferrite Core 11.4 Mutual Inductance 11.4.1 Theory 11.4.1.1 Magnetic Description 11.4.1.2 Circuit Theory 11.4.1.3 Modelling Mutual Inductance in LTspice 11.5 Power Transformers 11.5.1 Magnetics 11.5.1.1 Load Current Referred to the Primary 11.5.1.2 Magnetizing Current 11.5.2 Special Transformers 11.5.2.1 Autotransformer 11.5.2.2 Current Transformer 11.5.2.3 Audio Transformers 11.5.3 Models for Manual Analysis 11.5.3.1 Secondary Circuit Model for Manual Analysis 11.5.3.2 Primary Model 11.5.3.3 Load Referred to the Primary 11.5.3.4 Measuring Parameters 11.5.4 LTspice Models 11.5.4.1 Linear Model 11.5.4.2 Non-linear Models 11.6 Summary Chapter 12: LR and LCR Circuits 12.1 Introduction 12.2 Inductors 12.2.1 Energy Stored in an Inductor 12.2.2 Inductors in Series and Parallel 12.2.3 Time Response of an Inductor 12.2.4 Frequency Response of an Inductor 12.2.4.1 Reactance and Impedance of an Inductor 12.3 Settling Time 12.3.1 Pulse Train Input 12.3.2 Sine Wave Train Input 12.4 Bridges to Measure Inductance 12.4.1 The Maxwell Bridge 12.4.2 The Hay´s Bridge 12.4.3 The Owen Bridge 12.4.4 Anderson Bridge 12.5 Power Supply Filters 12.5.1 Capacitor Input 12.5.1.1 Ripple Voltage 12.5.2 Capacitor Input Filter 12.5.3 Inductor Input Filter 12.6 LR Filters 12.6.1 Cascaded LR Filters 12.6.1.1 Cascaded LR Low-Pass Filter 12.6.1.2 Cascaded High-Pass Filter 12.6.1.3 Cascaded Band-Pass Filter 12.6.2 Bridged-T Filters 12.6.2.1 With Series Inductors 12.6.2.2 Bridged-T with Series Resistors 12.7 Impedance Matching 12.7.1 LC Matching 12.7.1.1 Design Method 12.8 Crystals 12.8.1 Equivalent Circuit 12.8.2 Parameter Extraction and LTspice Model 12.9 Assorted Circuits 12.9.1 Electromagnetic Interference (EMI) Filter 12.9.1.1 Common Mode and Differential Mode 12.9.1.2 Capacitor Types 12.9.2 Power Factor Correction 12.9.2.1 Real and Apparent Power 12.9.3 LCR Notch Filter 12.9.4 Interrupted Continuous Wave Transmission 12.10 ESD Simulation IEC 61000-4-2 12.11 Loudspeakers and Crossovers 12.11.1 Loudness 12.11.2 Driver Construction 12.11.2.1 Multi-driver Systems 12.11.3 Thiele-Small Driver Parameters 12.11.3.1 Electrical Parameters 12.11.3.2 Fundamental Mechanical Parameters 12.11.3.3 Small-Signal Parameters 12.11.3.4 Large-Signal Parameters 12.11.4 Equivalent Circuits 12.11.4.1 Component Formulae 12.11.5 Enclosures 12.11.6 Crossovers 12.12 Summary Chapter 13: LCR Tuned Circuit 13.1 Introduction 13.2 Series Tuned Circuit 13.2.1 Frequency Response 13.2.1.1 Impedance 13.2.1.2 Resonant Frequency for Maximum Current 13.2.1.3 Resonant Frequency for Maximum Voltage 13.2.1.4 Resonance Frequency for Minimum Voltage 13.2.1.5 3 dB Points 13.2.1.6 Q-Factor 13.2.1.7 Voltage Cusp 13.2.1.8 Power Dissipation 13.2.1.9 Off-Resonance Response 13.2.1.10 Inductor with Parallel Resistor 13.3 Series Tuned Circuit Time Response 13.3.1 The Differential Equation 13.3.1.1 Series Circuit Decay Factor and Damping Ratio 13.3.2 Damping Conditions 13.3.2.1 Overdamped Current (D >0) 13.3.2.2 Critically Damped Current (D = 0) 13.3.2.3 Under Damped Current (D < 1) 13.3.3 Voltages 13.3.3.1 Overdamped 13.3.3.2 Critically Damped 13.3.3.3 Underdamped 13.3.3.4 Response with Precharged Capacitor 13.4 Parallel Tuned Circuit 13.4.1 Frequency Response 13.4.1.1 Impedance 13.4.1.2 Resonant Frequency 13.4.1.3 3 dB Points 13.4.1.4 Q-Factor 13.4.1.5 Off-Resonance Response 13.5 Parallel Resonance Damping 13.5.1 Including a Parallel Resistor 13.5.1.1 Damping Characteristic Equation 13.5.1.2 Decay Factor and Critical Damping 13.5.1.3 Overdamped Currents (α>ωn) 13.5.1.4 Critically Damped (α = ω0) 13.5.1.5 Underdamped 13.5.2 Including the Resistance of the Inductor 13.5.2.1 Self-Resonance of an Inductor 13.5.2.2 Resonant Frequency 13.5.2.3 Q-Factor and 3 dB Points 13.5.2.4 Damping 13.6 Summary Chapter 14: The Fourier Series and Fourier Transform 14.1 Introduction 14.2 The Fourier Series 14.2.1 The Concept 14.2.2 Harmonics and DC 14.2.3 Trigonometrical Form Derivation of the Coefficients 14.3 Simulation of Common Waveforms 14.3.1 Constant Waveform f(x) = k 14.3.2 The Triangular Wave Sawtooth Isosceles Triangular Scalene Triangular Wave 14.3.3 Square Waves The Gibb´s Phenomenon A Different Approach Square Wave as Cosines Square Wave with No DC Rectangular Waves 14.3.4 The Parabola 14.3.5 Full-Wave Rectified Sine Wave 14.4 The Exponential Form 14.4.1 Exponential Coefficients 14.4.2 Rectangular Wave Using the Exponential Form 14.5 Arbitrary Waveforms 14.5.1 Fractional Waveforms Ramp Half-Wave Rectified Sine 14.5.2 Piecewise Waveforms Manipulating Ramps Using Parabolas 14.6 Aperiodic Signals 14.6.1 The Sinc Function Rectangular Wave as Sinc Function 14.6.2 Aperiodic Pulse Duty Cycle and Pulse Height 14.6.3 Impulse Response Infinite Impulse 14.6.4 The Continuous Fourier Transform The Inverse Fourier Transform Fourier Transform Tables 14.7 The Discrete Fourier Transform (DFT) 14.7.1 Selecting a Harmonic Selectivity of the Picking Frequency Detecting the Harmonics 14.7.2 Finding the Amplitude Using Sine and Cosine The Exponential Factor ej2π 14.7.3 Sampling Rate and Data Points Aliasing and the Nyquist-Shannon Sampling Rate Run Time The DFT Equation The DFT Matrix Errors 14.8 The Fast Fourier Transform 14.8.1 LTSpice and the FFT The FFT Dialogue fromtran.´ Analysis
Data Density
Saving the Data
The Impulse Response
14.9 Summary
Chapter 15: Passive Filters
15.1 Introduction
15.2 Nyquist Plot
15.2.1 LTspice and the Nyquist Plot
Creating a Nyquist Plot
Making Measurements
15.2.2 Real and Imaginary Parts
Using the Laplace `s´ Form
15.2.3 Second Order Filters
15.3 Pole-Zero (s-Domain) Analysis
15.3.1 First-Order Systems
Low-Pass Filter
High-Pass Filter
15.3.2 Cascaded Second-Order Filters
Low-Pass Filter
High-Pass Filter
Band-Pass Filter
15.3.3 LCR Filters
Transfer Function and Roots
Pole Positions
15.3.4 LCR Filter Types
Low-Pass LCR Filter
High-Pass LCR Filter
Band-Pass LCR Filter
Band-Stop Filter
More Filters
15.4 LC Filters
15.4.1 Filter Prototypes
Image Impedance
T- Filter
Pi - Filter
Propagation Coefficient
Filter Characteristics
15.4.2 Constant-K Filters
Low Pass Constant-K Filter
High-Pass Constant-K Filter
Band-Pass Constant-K Filters
Band-Stop Constant-K Filter
15.4.3 M-Derived Filters
Low-Pass m Filter
High-Pass m Filter
Band-Pass and Band-Stop m Filters
15.4.4 Combined Filters
15.5 Tuned-Circuit Filters
15.5.1 Double-Tuned Band-Pass Filter
Analysis
15.6 Multi-stage Filters
15.6.1 Design
15.6.2 Butterworth Low-Pass Filter
15.6.3 Chebyshev Low-Pass Filter
15.6.4 Elliptic Filters
15.6.5 Transformation of Low Pass to High Pass, Band Pass and Band Stop
15.6.6 All-Pass Filters
15.6.7 Sensitivity
15.7 Summary
Index